Empirical likelihood for non-degenerate U-statistics

Abstract

Standard empirical likelihood for U-statistics is too computationally expensive. To overcome this computational difficulty, we reformulate the non-degenerate U-statistics as a sample mean of some "pseudo" observations in this paper, and show that the empirical log-likelihood ratio has an asymptotic chi-squared distribution under the second moment condition. The method is extremely simple to use, and yet provide better coverage accuracy in general than other alternative methods from our simulation studies.Empirical likelihood Confidence interval U-statistics